Answer:
- A = arccos((b² +c² -a²)/(2bc)) . . . . 'a' = longest side
- B = arcsin(b/a·sin(A))
- C = 180° -A -B
Explanation:
You want to know how to solve a triangle when three sides are given.
Law of cosines
The law of cosines can tell you an angle of a triangle when three sides are given. For example, the equation can be solved to give angle A as ...
A = arccos((b² +c² -a²)/(2bc))
It is convenient to solve for the largest angle, opposite the longest side. This removes any ambiguity when the Law of Sines is used to find another angle in the triangle.
Law of sines
When an angle and its opposite side are known, another angle can be found using the Law of Sines. This can be expressed as ...
sin(B)/b = sin(A)/a . . . . . . law of sines
B = arcsin(b/a·sin(A)) . . . . . solved for angle B
Angle sum theorem
You can use either of the above methods to find the third angle, but perhaps the easiest is to make use of the angle sum theorem. The sum of angles in a triangle is 180°, so the third angle will be the difference between 180° and the sum of the other two.
C = 180° -A -B
__
Additional comment
As always, values of any intermediate results (angles A and B, for example) should be maintained at best calculator precision until all values have been calculated. Rounding is appropriate only then.
The Law of Cosines can be used to find any or all of the angles. We judge using the Law of Sines to require less work after one angle is known. If you're doing the calculations in a spreadsheet, using the same formula for all cases might make life easier.
<95141404393>